Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the twodigit number?

Let the unit place digit of a two-digit number be x.
Therefore, the tens place digit = 9-x
2-digit number = 10 x tens place digit + unit place digit
Original number = 10(9-x)+x
According to the question, New number = Original number + 27
⇒ 10x+(9-x)=10(9-x)+x+27 ⇒ 10+9-x=90-10x+x+27
⇒ 9x+9=117-9x ⇒ 9x+9x=117-9
⇒ 18x = 108
⇒ x=108/18=6
Hence, the 2-digit number = 10(9-x)+x=10(9-6)+6=10 x 3 + 6 = 30+6 =36

Class 8 Maths Chapter 2 Exercise 2.4 Solution in Video

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